The fate of magnetically charged black holes

The magnetically charged Reissner-Nordström black hole solutions of Maxwell-Einstein theory cannot evaporate completely, because their Hawking temperature tends to zero as their mass to charge ratio approaches unity. This situation changes when these solutions are considered in the context of a non-Abelian gauge theory containing nonsingular magnetic monopoles. If the horizon is sufficiently small, the Reissner-Nordström solution develops a classical instability and evolves into a new type of magnetically charged black hole solution. The temperature of these new solutions increases monotonically as the horizon contracts, so that there is no obstacle to the complete evaporation of a magnetically charged black hole.     

Rotating hairy black holes

We construct stationary black-hole solutions in SU(2) Einstein-Yang-Mills theory which carry angular momentum and electric charge. Possessing nontrivial non-Abelian magnetic fields outside their regular event horizon, they represent nonperturbative rotating hairy black holes.     

Global charges of stationary non-Abelian black holes

We consider stationary axially symmetric black holes in SU(2) Einstein-Yang-Mills-dilaton theory. We present a mass formula for these stationary non-Abelian black holes, which also holds for Abelian black holes. The presence of the dilaton field allows for rotating black holes, which possess nontrivial electric and magnetic gauge fields, but do not carry a non-Abelian charge. We further present a new uniqueness conjecture.     

Stable monopole and dyon solutions in the einstein-yang-mills theory in asymptotically anti-de sitter space

A continuum of new monopole and dyon solutions in the Einstein-Yang-Mills theory in asymptotically anti-de Sitter space are found. They are regular everywhere and specified by their mass and their non-Abelian electric and magnetic charges. A class of monopole solutions which have no node in non-Abelian magnetic fields is shown to be stable against spherically symmetric linear perturbations.     

Dyonic String-Like Solution in a Non-Abelian Gauge Theory with Two Potentials

Axially symmetric dyon solutions of a non-Abelian gauge theory model with two potentials are sought. While seeking axially symmetric (flux tube like solutions) for the model, we stumbled upon an exact solution which represents an infinite string-like dyonic configuration with cylindrical symmetry.     

Quasinormal modes of non-Abelian hyperscaling violating Lifshitz black holes

We study the quasinormal modes of scalar field perturbations in the background of non-Abelian hyperscaling violating Lifshitz black holes. We find that the quasinormal frequencies have no real part so there is no oscillatory behavior in the perturbations, only exponential decay, that is, the system is always overdamped, which guarantees the mode stability of non-Abelian hyperscaling violating Lifshitz black holes. We determine analytically the quasinormal modes for massless scalar fields for a dynamical exponent \(z=2\) and hyperscaling violating exponent \(\tilde{\theta }>-2\). Also, we obtain numerically the quasinormal frequencies for different values of the dynamical exponent and the hyperscaling violating exponent by using the improved asymptotic iteration method.     

Plane-wave solutions in higher-dimensional Kaluza-Klein theories

Exact solutions representing mixed plane-gravitational waves and planewaves of scalar fields and non-Abelian gauge fields in higher-dimensional Kaluza-Klein theories are obtained under the generalized higher-dimensional harmonic condition. Two special cases are discussed.     

There are no Magnetically Charged Particle-like Solutions of the Einstein Yang-Mills Equations for Models with an Abelian Residual Group

We prove that there are no magnetically charged particle-like solutions for any model with an Abelian residual group in Einstein Yang-Mills, but for the non-Abelian models the possibility remains open. An analysis of the Lie algebraic structure of the Yang-Mills fields is essential to our results. In one key step of our analysis we use invariant polynomials to determine which orbits of the gauge group contain the possible asymptotic Yang-Mills field configurations. Together with a new horizontal/vertical space decomposition of the Yang-Mills fields this enables us to overcome some obstacles and complete a dynamical system existence theorem for asymptotic solutions with nonzero total magnetic charge. We then prove that these solutions cannot be extended globally for Abelian models and begin an investigation of the details for non-Abelian models.     

Topological Dyons

Using a two potential approach, dyon solutions have been found in the temporal and non-temporal gauges for a non-Abelian theory. Both the charges, electric and magnetic, of the temporal dyon solution are topological, while for the non-temporal case both charges are partially topological.     

Classical solutions in Grassmannian σ-models

We study the generalisation of the CP ⁿ⁻¹ model in two-dimensional Euclidean space-time to Grassmannian σ-models having a non-Abelian gauge group. Some classes of classical solutions are displayed. It appears that the general solutions involve complicated constraints.     

Classical non-Abelian particle in the field of a rotating colored black hole

The Hamilton-Jacobi method is used to derive and investigate the equations of motion of a classical non-Abelian particle in the field of a rotating colored black hole.Astrophysical Institute, Kazakh Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 3–7, May, 1993.     

New non-Abelian effects on D-branes

We extend the Myers dielectric effect to configurations with angular momentum. The resulting time-dependent N D0 brane bound states can be interpreted as describing rotating fuzzy ellipsoids. A similar solution exists also in the presence of a RR magnetic field, that we study in detail. We show that, for any finite N, above a certain critical angular momentum is energetically more favorable for the bound state system to dissociate into an Abelian configuration of N D0 branes moving independently. We have investigated this problem in the low-energy expansion of the non-Abelian D brane action for generic N. In the case N=2 we find explicit solutions of the full non-Abelian Born–Infeld D brane dynamics, which remarkably have the same structure and confirm the features of the low-energy approximation. We further study D string configurations representing fuzzy funnels deformed by the magnetic field and by the rotational motion.     

Noncommutative versions of Born-Infeld theory

A new generalization of nonlinear Born-Infeld electrodynamics is proposed. It is inspired by the noncommutative geometry and a new interpretation of gauge theories. The variational principle introduced here leads to quite complicated nonlinear equations, which can be solved numerically in certain cases. The spherically symmetric ansatz is analyzed, and static finite-energy solutions are obtained via numerical integration. Then a pure Higgs sector Lagrangian is introduced by analogy with the non-Abelian Born-Infeld generalization. A spherically symmetric configuration and a time-dependent homogeneous field are investigated and qualitative behavior of solutions are discussed.     

Non-Abelian prolongations and complete integrability

The Estabrook-Wahlquist prolongation of a one-parameter family of evolution equations is carried out explicitly. It is shown that a non-Abelian prolongation algebra is obtained only for that parameter value for which the prolonged equation belongs to a known class of integrable equations. A Bäcklund transformation is constructed for the integrable case, and periodic, kink and bell-type solutions are displayed.     

Magnetic monopoles

These are notes of the first part of the lectures given at the JINR-ISU Baikal Summer School on Physics of Elementary Particles and Astrophysics (July 2010). I review classical monopole solutions of the SU(2) Yang-Mills-Higgs theory providing a pedagogical introduction into to the theory of non-Abelian monopoles both in the BPS limit and beyond of it. I briefly discuss monopole dynamics, the idea of the moduli space and some of the basic properties which are connected with the field theoretical aspects of these classical solutions.     

Six-Dimensional Superconformal Field Theories from Principal 3-Bundles over Twistor Space

We construct manifestly superconformal field theories in six dimensions which contain a non-Abelian tensor multiplet. In particular, we show how principal 3-bundles over a suitable twistor space encode solutions to these self-dual tensor field theories via a Penrose–Ward transform. The resulting higher or categorified gauge theories significantly generalise those obtained previously from principal 2-bundles in that the so-called Peiffer identity is relaxed in a systematic fashion. This transform also exposes various unexplored structures of higher gauge theories modelled on principal 3-bundles such as the relevant gauge transformations. We thus arrive at the non-Abelian differential cohomology that describes principal 3-bundles with connective structure.     

Sharp existence and uniqueness theorems for non-Abelian multiple vortex solutions

Vortices in non-Abelian gauge field theory play essential roles in the mechanism of color confinement and are governed by systems of nonlinear elliptic equations of complicated structure. In this paper, we present a series of sharp existence and uniqueness theorems for multiple vortex solutions of the non-Abelian BPS equations over R²${\mathbb{R}}^2$ and on a doubly periodic domain. Our methods are based on calculus of variations which may be used to analyze more extended problems. The necessary and sufficient conditions for the existence of a unique solution in the doubly periodic situation are expressed in terms of physical parameters involved explicitly.     

The existence of multi-monopole solutions to the non-Abelian,Yang-Mills-Higgs Equations for arbitrary simple gauge groups

We prove that for arbitrary simple gauge groups, the non-Abelian Yang-Mills-Higgs Equations on ³ in the Prasad-Sommerfield limit have at least a countably infinite set of distinct solutions. These solutions may be interpreted physically as configurations of widely spaced, non-interacting fundamental monopoles. The solutions are generically not spherically symmetric.Harvard University, John Parker FellowThis work is supported in part by the National Science Foundation under Grant No. PHY 79-16812     

QGP Kinetic Equations Beyond the Linear Response Theory

It is shown that the non-Abelian properties? of QGP can be got by studying the kinetic equations for QGP beyond the linear response theory. The non-Abelian interaction of the eigenmodes in QGP is found and two quantities describing the non-Abelian properties of QGP are given.